A coherent sequent true in all set models of a coherent theory is coherently derivable. A generic underivable sequent remains false after the Boolean cover by a generic quasi-closed subtopos. Slice over its nonzero Boolean counterexample to show classical consistency of the theory with a named tuple satisfying the antecedent and negated consequent. The Henkin construction then gives a set-valued countermodel. This argument does not assume that every Boolean topos has points.
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